Many-body topology of fermionic symmetry-protected topological phases in one dimension

Chen-Shen Lee¹, Ken Shiozaki³, Chang-Tse Hsieh^1,2*

¹Department of Physics, National Taiwan University, Taipei, Taiwan
²Physics Division, National Center for Theoretical Science, National Taiwan University, Taipei, Taiwan
³Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan

* Presenter:Chang-Tse Hsieh, email:cthsieh@phys.ntu.edu.tw

We study short-range entangled many-body topological phases of fermions in the presence of charge conservation and chiral or reflection symmetry. We compute the many-body topological invariants, defined by applying the partial transpose or partial reflection to the system's ground state, for certain models of one-dimensional fermions with and without interactions, and see how these invariants vary under deformations among these models. As expected, gapped deformations exist when the topological invariants remain unchanged. Furthermore, for decomposable systems—those that can be decomposed into local and decoupled subsystems—we can assign specific real-space quantum numbers that match the many-body topological invariants, giving rise to bulk-boundary correspondence for systems with chiral symmetry and the bulk-center correspondence for systems with reflection symmetry. The correspondence in the latter case is justified using the Atiyah-Hirzebruch spectral sequence in generalized homology theory.

Keywords: topological phases of matter, many-body topological invariant, bulk-boundary correspondence, bulk-center correspondence